If $a$ and $b$ are real numbers, find the value of $b$ , if $(a + b) + 5 i = 9 + a i$ and given that $i^{2} = - 1$

4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

9

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 + 5 i

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5 + 4 i

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $4$
Given, $(a + b) + 5 i = 9 + a i$
Equating the real and imaginary parts, we get
$a + b = 9, a = 5$
Put $a = 5$ in $a + b = 9$
$\Rightarrow 5 + b = 9$
$\Rightarrow b = 4$

Suggest Corrections

Similar questions

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} - 7 & 5 + 3 i & \frac{2}{3} - 4 i 5 - 3 i & 8 & 4 + 5 i \frac{2}{3} + 4 i & 4 - 5 i & 9 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} - 7 & 5 + 3 i & \frac{2}{3} - 4 i 5 - 3 i & 8 & 4 + 5 i \frac{2}{3} + 4 i & 4 - 5 i & 9 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ ∣ \begin{matrix} - 5 & 3 + 5 i & \frac{3}{2} - 4 i 3 - 5 i & 8 & 4 + 5 i \frac{3}{2} + 4 i & 4 - 5 i & 9 \end{matrix} ∣ ∣ ∣ ∣ ∣

x, y \in R

(x + 2 y) + i (2 x - 3 y) = 5 - 4 i

(x + i y) + (7 - 5 i) = 9 + 4 i

x^{2} - y^{2} - i (2 x + y) 2 i

x

y

(x + i y) (7 - 5 i) = 9 + 4 i

Join BYJU'S Learning Program